Why are new smartphone processors hexa and octa-core, while consumer desktop CPUs are still often quad-core?

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4 fast cores, 4 slow cores

CPU's, just like car engines, are all about trade-offs. The two biggest ones are performance and efficiency. If you have a crazy 900hp v12 in your car you won't be driving very far before you have to fill up again. Same thing with CPU's, a super high-performance processor will mean your battery won't last very long.
On the other hand having a super efficient CPU that sips energy will give you great battery life but you might go crazy with how slow your phone will be.
Traditionally you got 4 cores somewhere in between those two options. A compromise of performance and efficiency. Now, with these 8 core processors for example, you get 4 high-performance cores and 4 slow but high-efficiency cores. That way when you're playing a mobile game or something you get the performance you want from the 4 fast cores. If you're just send text messages every now and then your phone switches to the slower cores to give you longer battery life.

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